Is the solid charged? A conductor? Can you be a little more transparent as to where you are going here? Need more to go on.Philip Koeck said:If a solid (a few nm diameter) was placed in vacuum inside a grounded hollow sphere, but without touching the sphere (zero gravity), qualitatively what would the potential inside this solid be on average? In other words I don't want to look so closely that I see the potential wells of the nuclei. Would an electron wave propagating through this solid experience a phase shift?
Philip Koeck said:The solid is not charged. As an example one could think of a piece of amorphous carbon.
The reason for my question is that I'm wondering about the usual explanation how an electron optical Zernike phase plate works. I can't quite make sense of it.
Philip Koeck said:what would the potential inside this solid be on average
Yes, I think that might be the explanation. The idea is that carbon has a "mean inner potential" of about 10 V compared to vacuum, so that a 200 keV electron wave going through 20 nm of carbon is phase shifted by pi/2 compared to one going through vacuum. That's how a phase plate for an electron microscope is supposed to work. If I think of a solid as a smeared out negative charge with positive charges distributed evenly in it I can't get that to work. The average charge density (averaged over sufficiently large volumes) would be about zero everywhere and I would expect a mean inner potential equal to that of vacuum (based on the Poisson equation). If instead I assume a negative surface charge balanced by a positive charge right below it one could get a positive inner potential (compared to vacuum).hutchphd said:Materials develop surface potentials that look like ~dipole layers for various reasons. If a material looks like a negative slab of stuff with thin positive surface (or vice-versa) it will phase shift the electron passing through. It can even produce resonances if the geometry matches. Does that help?
When a solid is electrically neutral, it means that the number of positive charges (protons) is equal to the number of negative charges (electrons) within the solid. This results in a net charge of zero, meaning the solid has no overall positive or negative charge.
The average potential inside an electrically neutral solid is calculated by dividing the total potential energy by the total number of charges within the solid. This gives an average value for the potential energy per charge within the solid.
The average potential inside an electrically neutral solid can be affected by the distribution of charges within the solid, the size and shape of the solid, and the material properties of the solid such as its conductivity and permittivity.
The average potential inside an electrically neutral solid is directly related to its electric field. The electric field is a measure of the force per unit charge, and the average potential is a measure of the potential energy per charge. Therefore, the electric field can be calculated by taking the derivative of the average potential with respect to distance.
No, the average potential inside an electrically neutral solid will always be zero. This is because, as stated earlier, an electrically neutral solid has an equal number of positive and negative charges, resulting in a net charge of zero. Therefore, the average potential, which is calculated by dividing the total potential energy by the total number of charges, will always be zero.